There are 26 red cards and 13 spades in a standard deck of 52 cards. The probability of drawing a red card or a spade in one draw is, therefore, 39 in 52. If you draw twocards, and the first is not red or spade, then the probability on the second draw is 39 in 51, otherwise it is 38 in 51.
Combining these two probabilities is easy. Just turn the problem around, and ask what is the probability of drawing two clubs? The answer is (13 in 52) times (12 in 51), which is 156 in 2652, or 1 in 17. Flip that answer over by subtracting it from 1, and you get a probability of drawing a red card or a spade in two draws of 16 in 17, or about 0.9412.
The probability of drawing a red card followed by a spade is (1 in 2) times (1 in 4), or 1 in 8, or 0.125. The probability of drawing a spade followed by a red card is (1 in 4) times (1 in 2), or 1 in 8, or 0.125. Since you have two distinct desired outcomes, add them together, giving a probability of drawing a red card and a spade of 0.25.
1/48 if there aren't jokers
It is 1/169 = 0.005917, approx.
Abolut 4 in208
2 in 52, or 1 in 26, or about 0.03846.
It is approx 0.44
The probability of drawing a diamond from a standard 52-card poker deck without jokers is 13/52, or 1/4. The probability of drawing a second diamond at that point would then be 12/51, for an overall probability of 12/212, or 3/53. This amounts to about a 5.88% chance.
The probability of drawing aces on the first three draws is approx 0.0001810
The probability of drawing a red card followed by a spade is (1 in 2) times (1 in 4), or 1 in 8, or 0.125. The probability of drawing a spade followed by a red card is (1 in 4) times (1 in 2), or 1 in 8, or 0.125. Since you have two distinct desired outcomes, add them together, giving a probability of drawing a red card and a spade of 0.25.
1/48 if there aren't jokers
4/221
It is 1/169 = 0.005917, approx.
Let's call the chance of drawing a 9 on the first draw P(A). Since there are four 9s, P(A) is 4/52. Probability of not drawing a 9 is 1-(4/52). Each draw is independent so we multiply the probabilities. The probability of EXACTLY one 9 in two draws if P(A)P(1-A)=12/169 which is a about .071
Abolut 4 in208
The probability of drawing three black cards from a standard pack depends on:whether the cards are drawn at random,whether or not the drawn cards are replaced before the next card is drawn,whether the probability that is required is that three black cards are drawn after however many draws, or that three black cards are drawn in a sequence at some stage - but not necessarily the first three, or that the first three cards cards that are drawn are black.There is no information on any of these and so it is not possible to be certain about the answer.The probability of drawing three black cards, in three random draws - without replacement - from a standard deck, is 0.1176 approx.
The probability of drawing any single card in a deck of 52 cards is 1 in 52. It does not matter if you replace it or not, unless you intend to make multiple draws. In the multiple draw case, each subsequent probability increases; 1 in 51, then 1 in 50, then 1 in 49, etc. As an example, the probability of drawing the seven of diamonds in five draws from a standard deck is 1 in 52 plus 1 in 51 plus 1 in 50 plus 1 in 49 plus 1 in 48. This adds up to about 1 in 10.
The probability of drawing two blue cards froma box with 3 blue cards and 3 white cards, with replacement, is 1 in 4, or 0.25.The probability of drawing one blue card is 0.5, so the probability of drawing two is 0.5 squared, or 0.25.